Guide to Principal Component Analysis

PCA is a buzz word which always pops up at many stages of Data Analysis for various uses. But what is really behind this Principal Component Analysis? What are the uses of it? Let’s see one by one.

First, let us understand what is done behind the screen called PCA. I have attached a Jupyter Notebook with examples at the bottom of the article.

Yes, you are correct, it is a 2D graph.

Yes, it is a 1D graph, because, for every x, the y value is the same.

Let’s move to a tricky question — if you can guess this one you have successfully pass the first step in PCA.

If you say 2D, nope that is wrong. It is 1D — What? But how?

Yes, if we rotate the axis a bit the data points will align as same as our previous case (Fig-2). This is done in following sub-steps,

One of the major uses of PCA is Dimensionality reduction. Assume you have dozens of features on your dataset. But unfortunately, we can only,

So somehow we need to reduce the noise of data and filter out the meaningful features for our task. This where the PCA comes in handy.

Intrinsic dimension is the number of features needed to approximate a dataset. This is the key idea behind the dimension reduction. If we need to reduce the dimension we should know which features we should select and which to neglect.

Usually, PCA in Sklearn will automatically find the number of Intrinsic Dimensions itself. It will consider PCA features with significant variance. We can also explicitly specify the number of components to be considered.

Sometimes python notebooks are not loading in GitHub properly. In such cases download the Notebook and open it using your local Jupyter environment.

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